I think I've got it.
George II -> Princess Mary -> Charles of Hesse -> Louise of Hesse -> Christian IX of Denmark -> George I of Greece and Denmark -> Princess Olga of Greece and Denmark -> Princess Elizabeth of Yugoslavia -> Catherine Oxenberg
So they definitely have George II as a common ancestor.
George II -> Princess Mary -> Charles of Hesse -> Louise of Hesse -> Christian IX of Denmark -> George I of Greece and Denmark -> Princess Olga of Greece and Denmark -> Princess Elizabeth of Yugoslavia -> Catherine Oxenberg
So they definitely have George II as a common ancestor.